The nontrivial kernel of Manturov-Nikonov map from classical braids to virtual braids
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908917631549440 |
|---|---|
| author | Liu, Yangzhou |
| author_facet | Liu, Yangzhou |
| contents | In 2022, V. O. Manturov and I. M. Nikonov \cite{Man22} constructed two composite maps, one of them is following: $$PB_{n+1} \overset{p_k}{\rightarrow} CPB_{n} \overset{f_d}{\rightarrow} VCB_{n}\oversetρ{\rightarrow} GL_n(\mathbb{Z}[t^{\pm 1},s^{\pm 1}])$$ In this paper, we prove that M-N is unfaithful if $k\geq 6$ since Burau kernel is a subgroup of M-N kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26851 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The nontrivial kernel of Manturov-Nikonov map from classical braids to virtual braids Liu, Yangzhou Geometric Topology 57K12, 20F36, 57M27 In 2022, V. O. Manturov and I. M. Nikonov \cite{Man22} constructed two composite maps, one of them is following: $$PB_{n+1} \overset{p_k}{\rightarrow} CPB_{n} \overset{f_d}{\rightarrow} VCB_{n}\oversetρ{\rightarrow} GL_n(\mathbb{Z}[t^{\pm 1},s^{\pm 1}])$$ In this paper, we prove that M-N is unfaithful if $k\geq 6$ since Burau kernel is a subgroup of M-N kernel. |
| title | The nontrivial kernel of Manturov-Nikonov map from classical braids to virtual braids |
| topic | Geometric Topology 57K12, 20F36, 57M27 |
| url | https://arxiv.org/abs/2603.26851 |